@user49685: Such limit arguments don't tell you anything unless you already know that the function $(x,y)\mapsto x^y$ is continuous everywhere you need it to be. And it isn't.
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Henning MakholmFeb 5 '13 at 12:49

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@user49685: $0^0$ doesn't "tend"; it contains no variables at all. The expression $f(x)^{g(x)}$ can tend to something, and if $f(x)\to 0$ and $g(x)\to 0$, then the limit of $f(x)^{g^(x)}$ can be called indeterminate. But there can't be any tending without a variable to vary.
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Henning MakholmFeb 5 '13 at 13:35